On Neyman-Pearson optimality of binary neural net classifiers

In classical binary statistical pattern recognition optimality in Neyman-Pearson sense, achieved by a (log) likelihood ratio based classifier, is often desirable. A drawback of a Neyman-Pearson optimal classifier is that it requires full knowledge of the (quotient of the) class-conditional probability densities of the input data, which is often unrealistic. The design of neural net classifiers is data driven, meaning that no explicit use is made of the class-conditional probability densities of the input data. In this paper a proof is presented that a neural net can also be trained to approximate a log-likelihood ratio and be used as a Neyman-Pearson optimal, prior-independent classifier. Properties of the approximation of the log-likelihood ratio are discussed. Examples of neural nets trained on synthetic data with known log-likelihood ratios as ground truth illustrate the results.